Suboptimal constrained bilinear control of a class of hyperbolic PDEs applied to heat transport in solar collector parabolic troughs

Solar energy constitutes one of the most abundant energy resources. Advanced control techniques can have an important role in the promotion of such renewable energies by improving their efficiency. In this paper, a finite-horizon optimal controller is proposed to solve the problem of tracking a prescribed temperature profile in a solar collector parabolic trough (SC). The SC is represented by a first-order hyperbolic PDE, where the control input is the pump flow rate which generates a bilinear control problem. Based on the control parameterization approach, an approximate optimal controller is designed in the infinite-dimensional framework. The gradients of the cost function are formulated analytically, based on the sensitivity method. The approximate nonlinear optimization problem is then solved numerically using sequential quadratic programming. Simulation results illustrate the effectiveness of the designed control technique.